American students struggle in math.
The latest results of an international exam given to teenagers ranked the USA ninth in reading and 31st in math literacy out of 79 countries and economies. America has a smaller-than-average share of top-performing math students, and scores have essentially been flat for two decades.
One likely reason: U.S. high schools teach math differently than other countries.
Classes here often focus on formulas and procedures rather than teaching students to think creatively about solving complex problems involving all sorts of mathematics, experts said. That makes it harder for students to compete globally, be it on an international exam or in colleges and careers that value sophisticated thinking and data science.
There is a growing chorus of math experts who recommend ways to bring America’s math curriculum into the 21st century to make it more reflective of what children in higher-performing countries learn. Some schools experiment with ways to make math more exciting, practical and inclusive.
“There’s a lot of research that shows when you teach math in a different way, kids do better, including on test scores,” said Jo Boaler, a mathematics professor at Stanford University who is behind a major push to remake America’s math curriculum.
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Here are some ideas for improving it:
Stop teaching the ‘geometry sandwich’
Most American high schools teach algebra I in ninth grade, geometry in 10th grade and algebra II in 11th grade – something Boaler calls “the geometry sandwich.”
Other countries teach three straight years of integrated math – I, II and III — in which concepts of algebra, geometry, probability, statistics and data science are taught together, allowing students to take deep dives into complex problems.
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In higher-performing countries, statistics or data science – the computer-based analysis of data, often coupled with coding – is a larger part of the math curriculum, Boaler said. Most American classes focus on teaching rote procedures, she said.
Next year, Boaler and a research team plan to recommend that California phase out the algebra-geometry pathway in favor of integrated math for all students – something she pitched to education leaders across the state.
Some states, such as Utah, have made the switch. The Common Core academic standards, a version of which most states adopted, say high school math can be taught in either format.
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The move requires extra time and resources to train teachers. Georgia mandated high schools teach integrated math starting in 2008. After pushback from teachers and parents, it gave schools the option to go back to the old sequence in 2016. In one large survey, Georgia teachers said they didn’t want to specialize in more than one math area.
The podcast Freakonomics featured an episode in October about the peculiarities of America’s math curriculum. Hosted by University of Chicago economist Steve Levitt, it highlighted Boaler’s work and garnered significant feedback, given the specificity of the topic, Levitt told USA TODAY.
Levitt is engaged in the movement to upend traditional math instruction. He said high schools could consider whittling down the most useful elements of geometry and the second year of algebra into a one-year course. Then students would have more room in their schedules for more applicable math classes.
“When you talk to people within the math education industry, they call that insanely radical,” Levitt said. “I think most parents would not consider it radical to teach only the best of two subjects that most people don’t like that much.”
Make more room for data science
“Ninety percent of the data we have in the world right now was created in the past two years,” Boaler said. “We’re at a point in this world where things are changing, and we need to help students navigate that new world.”
Other countries act more quickly on that idea. Estonia students ranked first among European countries in mathematics, as well as reading and science, on the 2018 Programme for International Student Assessment. Many factors may have helped: The country offers high-quality early childhood education to all kids, class sizes are small, and there’s little high-stakes testing, leaving more time for instruction.
Unlike other countries, Estonia teaches computer programming at all grade levels – a strategy started in the upper grades in the late ’90s and extended to elementary schools around 2012. The country is experimenting with adopting a new computer-based math curriculum.
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In the USA, about 3,300 students this year in 15 Southern California school districts are taking a new Introduction to Data Science course that features data and statistics, real-life data collection and coding to analyze the data. The course was developed by the University of California-Los Angeles and the LA Unified School District, and it counts as a statistics credit.
The class features a scripted curriculum with engaging exercises, such as having students record how much time they spend grooming themselves, then comparing that with national data collected for the American Time Use survey.
Teachers are trained to teach the class, as many haven’t been exposed to programming before, said Suyen Machado, director of the Introduction to Data Science project.
Students who took the new course showed significant growth in their statistical understanding over the year, studies show. Students said they felt learning to code was a valuable skill.
“A lot of students report that they find the content is more applicable to real life,” Machado said. “One of the more challenging things about the course is learning programming. They say it’s hard, but they want to do it.”
Stop splitting up students so much, and don’t hasten the curriculum
Over the years, some schools have sought to raise math achievement by pushing algebra down to eighth grade. High-flying students may adapt and have room to take more advanced high school classes. Hastening the curriculum can widen the gulf in achievement between lower-performing students, including those who are economically disadvantaged and racial minorities.
The practice reflects a long-standing feature of American math education: As early as middle school, students are often split into “tracks” in ways that predetermine who will take advanced classes in high school. The advanced classes are often full of students who are white or Asian and attend suburban schools – while black and Latino students continue to be underrepresented, research shows.
About six years ago, San Francisco’s school leaders sought to tackle the problem. They halted teaching algebra I in eighth grade. Students take the same three-year sequence of math courses in middle school, and everyone is enrolled in mixed-ability classrooms, said Lizzy Hull Barnes, math supervisor at the San Francisco Unified School District.
In high school, all students take ninth grade algebra and 10th grade geometry. After that, students can choose their path: Some may pick algebra II, others may choose a course combining algebra II and pre-calculus. Some may accelerate to AP statistics.
Before the change, 40% of graduating seniors in San Francisco had to repeat algebra I in their academic careers. For the Class of 2019, the first cohort of students to follow the new sequence, just 8% of students had to repeat the course.
The changes led to a major increase in disadvantaged students enrolling in higher-level math classes as juniors and seniors, Barnes said. Boosting the success of black and Latino students did not harm the progress of high-achieving white and Asian students.
“It’s been a seismic shift,” Barnes said.
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Change the way elementary teachers think about math
Improving the math aptitude of older students in the USA is connected to messages students hear about why math is important and who’s good at it when they’re younger.
Those messages often come from their elementary school teachers, many of whom didn’t like math as students themselves.
“Math phobia is real. Math anxiety is real,” said DeAnn Huinker, a professor of mathematics education at the University of Wisconsin-Milwaukee who teaches future elementary and middle school teachers.
New research suggests that when teachers improve their attitude toward math, it can help to raise student test scores. At Stanford, Boaler and her team designed an online course for teachers featuring research showing anyone can learn math with enough practice, intelligence isn’t fixed and math is connected to all sorts of everyday activities.
They recruited fifth grade teachers from a county in central California to take and discuss the course. Within a year, the participating teachers’ students posted significantly higher state math scores compared with previous years. The jumps were particularly significant for girls and low-income students, Boaler said.
“They thought they had to teach procedures, and then realized they could teach in this open, visual, creative way,” Boaler said. “A lot of research studies suggest that it takes a long time for changes to come about. In this one, it was quick.”
Make high school math reflect real life
Beyond data science, some districts design courses that include more real-world math and topics such as financial algebra and mathematical modeling.
The approach has led other countries to success. Teens in the Netherlands post some of the strongest math scores in the world on the PISA assessment. That’s largely because the exam prioritizes the application of mathematical concepts to real-life situations, and the Dutch teach math rooted in reality and relevant to society.
Some longtime Dutch math experts were involved in the design of PISA, which began in 2000 and is given every three years to a sample of 15-year-old students in developed countries and economies.
At Sweetwater High School in Chula Vista, California, math teacher Melody Morris teaches a new 12th grade course that explores topics such as two-player games, graph theory, sequences and series and cryptography. The course, called Discrete Math, was developed through a partnership with San Diego State University.
In one exercise, Morris teaches students to play a capture-the-flag style game featured on the television show “Survivor.” They learn that by using math, they can win every time.
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“Their typical response is: ‘This is math?’ ” Morris said. “They think it’s about playing games and having fun. But what they’re really learning is how to break down large problems into small ones and how to make hypotheses and test them.”
Students at Sweetwater still rise up through the traditional “geometry sandwich” from ninth through 11th grades. Morris said many who choose her class senior year find themselves much more engaged in the material. They develop a toolkit that will allow them to approach any problem in life, Morris said.
“A lot of what we’re building is habits of mind,” she said.
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